The origin of the buky letterform is genuinely contested, and it is the clearest small case of the larger argument about how Cyrillic was assembled.
One camp reads it as a differentiated beta. On this account whoever made the alphabet took the Greek letter twice: once in its plain uncial form for v, which is what beta had come to mean in spoken Byzantine Greek, and once modified for b, which Greek could no longer supply. The two Cyrillic letters would then be siblings, made at the same moment out of one Greek model, and their visible resemblance is the evidence.
The other camp derives buky from the Glagolitic letter of the same name, redrawn in a Greek manner to sit on a Greek page. The evidence here is structural rather than visual: buky carries no numeral, which is the signature of the letters that came from outside the Greek series, and the Glagolitic alphabet already had a fully worked out sign for b that a maker of Cyrillic would have had no reason to discard.
A third position holds that neither derivation can be demonstrated, because the shapes involved are too simple for resemblance to count as descent and because no exemplar of either alphabet survives from the century in which the question was decided. That is not a compromise between the first two positions. It is a claim that the evidence available cannot bear the weight put on it, and on the present manuscript record it is difficult to refute.